Calculate the number of atoms present per unit cell if the product of density and volume of the unit cell is $1.8 \times 10^{-22} \ g$. [Mass of an atom $= 4.5 \times 10^{-23} \ g$]

Calculate the number of unit cells in $58.5 \, g$ of $NaCl$ crystallizing in an $fcc$ structure. $(NaCl = 58.5 \, g/mol)$

Calculate the volume of the unit cell for an element having a molar mass of $92 \ g \ mol^{-1}$ that forms a $bcc$ structure,given $\left[\varrho \times N_{A} = 5.0 \times 10^{24} \ g \ cm^{-3} \ mol^{-1}\right]$.

The density of chromium metal is $7.2 \, g \, cm^{-3}$. If the edge length of the unit cell is $289 \, pm$, determine the type of unit cell (Simple Cubic, Body-Centered Cubic, or Face-Centered Cubic). [Atomic mass of $Cr = 52 \, a.m.u.$, $N_A = 6.02 \times 10^{23} \, mol^{-1}$]

Calculate the number of particles present per unit cell if the mass of a particle is $8.0 \times 10^{-23} \ g$ and the product of density and volume of the unit cell $(\varrho \times a^3)$ is $3.2 \times 10^{-22} \ g$.

For a crystal, the angle of diffraction $(2 \theta)$ is $90^{\circ}$ and the second order line has a $d$ value of $2.28 \ \text{Å}$. The wavelength (in $\text{Å}$) of $X$-rays used for Bragg's diffraction is